Abstract
We study a generalized non-local theory of gravity which, in specific limits, can become either the curvature non-local or teleparallel non-local theory. Using the Noether symmetry approach, we find that the coupling functions coming from the non-local terms are constrained to be either exponential or linear in form. It is well known that in some non-local theories, a certain kind of exponential non-local couplings is needed in order to achieve a renormalizable theory. In this paper, we explicitly show that this kind of coupling does not need to be introduced by hand, instead, it appears naturally from the symmetries of the Lagrangian in flat Friedmann–Robertson–Walker cosmology. Finally, we find de Sitter and power-law cosmological solutions for different non-local theories. The symmetries for the generalized non-local theory are also found and some cosmological solutions are also achieved using the full theory.
Highlights
Apart from its remarkable success to interpret cosmological observations, the -cold dark matter ( CDM) model still lacks according a satisfactory explanation to the issue why the energy density of the cosmological constant is so small if compared to the vacuum energy of the Standard Model (SM) of particle physics
Motivated by an increasing amount of studies related to nonlocal theories, here we proposed a new generalized nonlocal theory of gravity including curvature and teleparallel terms
For a flat FRW cosmology, using the Noether symmetry approach, the coupling functions can be selected directly from the symmetries for the various models derived from the general theory
Summary
Apart from its remarkable success to interpret cosmological observations, the -cold dark matter ( CDM) model still lacks according a satisfactory explanation to the issue why the energy density of the cosmological constant is so small if compared to the vacuum energy of the Standard Model (SM) of particle physics. This is generalized to a more complex action as soon as we substitute T with an arbitrary function of this, f (T ) This theory can present problems that are non-Lorentz invariant and because a covariant formulation of f (T ) gravity is still not very well accepted since the spin connection is a field without dynamics. Recently there was proposed a similar kind of non-local gravity based on the torsion scalar T In this theory, the action reads as follows [36]:. Non-local teleparalell gravity given by the action (10) is recovered if χ = 0 and f ( −1T, −1 B) = f ( −1T ) Starting from this theory, we can construct a scalar tensor analog by using Lagrange multipliers and we can constrain the distortion function f by the so-called Noether symmetry approach [37].
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